For a complex Lie group $G$ with real form $G_0\subset G$, we prove that any Hamiltionian automorphism $\phi$ of coadjoint orbit $\mathcal O_0$ $G_0$ whose connected components are simply connected, may be approximated by holomorphic O_0$-invariant symplectic the corresponding in sense Carleman, provided O$ is closed. In course proof, establish Hamiltonian density property for closed orbits all...

Let ‖⋅‖ be a norm on RN and let M closed C1-submanifold of RN. Consider the pointed metric space (M,d), where d is given by d(x,y)=‖x−y‖, x,y∈M. Then Lipschitz-free F(M) has approximation property.

In this paper, we have obtained an approximation result in the Generalized Finite Element Method (GFEM) that reflects the global approximation property of the Partition of Unity (PU) as well as the approximability of the local approximation spaces. We have considered a GFEM, where the underlying PU functions reproduce polynomials of degree l. With the space of polynomials of degree k serving as...

We give an overview of a number of algebraic multigrid methods targeting finite element discretization problems. The focus is on the properties of the constructed hierarchy of coarse spaces that guarantee (two-grid) convergence. In particular, a necessary condition known as “weak approximation property,” and a sufficient one, referred to as “strong approximation property,” are discussed. Their ...

We extend the abstract frameworks for the multigrid analysis for nonconforming finite elements to the case where the assumptions of the second Strang lemma are violated. The consistency error is studied in detail for finite element discretizations on domains with curved boundaries. This is applied to prove the approximation property for conforming elements, stabilized Q1/P0elements, and nonconf...